Here's that vector-space code, formatted better. -- Maybe is handled like the Maybe-of-Sum monoid instance AdditiveGroup a => AdditiveGroup (Maybe a) where zeroV = Nothing Nothing ^+^ b' = b' a' ^+^ Nothing = a' Just a' ^+^ Just b' = Just (a' ^+^ b') negateV = fmap negateV {- Alexey Khudyakov wrote: I looked through vector-space package and found lawless instance. Namely Maybe's AdditiveGroup instance It's group so following relation is expected to hold. Otherwise it's not a group.
x ^+^ negateV x == zeroV
Here is counterexample:
let x = Just 2 in x ^+^ negateV x == zeroV False
I think it's not possible to sensibly define group instance for Maybe a at all.I see that the problem here is in distinguishing 'Just zeroV' fromNothing. I could fix the Just + Just line to use Nothing instead of JustzeroV when a' ^+^ b' == zeroV, although doing so would require Eq a andhence lose some generality. Even so, the abstraction leak would probablyshow up elsewhere.Hm. -}